For those who desire a dispassionate view of death-row justice, let them know that no axe will be ground here,
and lest there be any well-intentioned persons who do not perceive the difference between polemic and analysis, style and substance, pomposity and eloquence, let them
know that it is always the latter to which we aspire, never the former. For those who endure the stringency of this essay, let them also know they
will discover that justice depends on geography, that much of America is fair, and that bias on death row affects mostly
whites.

We are indebted to Rev. Jesse Jackson for inspiring a back-of-the-envelope calculation that evolved into this essay. When
La Griffe du Lion opened the cover of Jackson's book, Legal Lynching: Racism, Injustice and the Death Penalty, we
recognized immediately the hand of illogic and bombast we have come to expect. When Jackson submits that, "African
Americans make up 25 percent of Alabama's population, yet of Alabama's 117 death row inmates, 43 percent are black,"
we know that not even he accepts this tired argument as evidence of racial discrimination. It is quintessential Jackson,
offering pabulum to his public.

Death row cannot be a racial mirror of America, because blacks commit murder at a higher rate than whites - seven to eight
times higher. Yet, the simplicity of Jackson's racial-mirror argument is appealing. Cleaned up to account for differential
homicide rates, it becomes a powerful tool for assessing bias. This we have done and will now elaborate.

Along the path to death row, race can insinuate itself at any
point, from the prosecutor's decision to seek the death penalty, to the jury's
verdict (recall O.J.) or recommendation of a death sentence. Of course, we could
argue that sex or appearance might exert similar influences, and we would
probably be correct.

Chasing discrimination at
every turn is burdensome and loaded with statistical pitfalls. Variables are
many - controlling them a challenge.
Even the choice of dependent variable may not be obvious. That is why we are
indebted to Rev. Jackson. His racial-mirror argument considers none of this. It cuts
to the bottom line: the color of death row. It disregards detail,
seeing only the sum of bias on the road to execution. It is
an "integral" approach, and asks only one question: Given black and white homicide rates, is death row too black, too white
or just right?Uncorrected for differential murder rates, the answer is: too black. Corrected, the answers vary and
may sometimes surprise.

The Color of Death Row without Bias Racial and ethnic groups behave differently in many ways. Crime is one of them, particularly violent crime, and specifically
murder. Consider, for example, per capita murder-rates by race, derived from FBI and Census Bureau data and shown in
Table 1.

Table 1. Murder and non-negligent manslaughter per 100,000 members of the offender's group (1996)

Characteristics of victim

Characteristics of Offender

White

Black

White

1.60

1.71

Black

0.114

10.91

Data are derived from the FBI publication, Crime in the United States, 1996, and population estimates by the U.S. Census Bureau. Included only are
single victim and offender crimes.

Table 1 shows us that
patterns of violent behavior resulting in death are vastly different for whites and blacks. The differences are essential to a correct
interpretation of death-row statistics. First notice that blacks kill mostly blacks, whites
kill mostly whites, white-on-black murder
is negligibly small, and most important for our purpose, the per capita murder rate for blacks is about 7.4 times that of whites. That
is, A black is more than 7 times as likely to commit murder as a white. From these and similar data, we can model death row as it
would exist in a bias-free justice system. Its racial complexion will serve as a benchmark.

Suppose, in a given state, there are a total of N black and white inmates on death row. The probability, Pn , that n are black is given by
the binomial distribution,

where pB and pW are the probabilities that a random inmate is black or white, respectively. We have isolated a black and white
universe so that pB + pW = 1.

Equation (1) is a yardstick for measuring racial equity. It describes death row as it would exist
in a racially-neutral justice system.
We can use it to find the probability of a particular racial mix on death row.

More useful is the probability that the number of blacks
(or whites) falls within a specific range. We obtain this by summing (1) over
that range. Thus, the probability, Pab , that the number of
blacks on death row falls in the interval [a , b] is

Another useful quantity is the most probable number of blacks on death row. This is the value of n that yields the largest Pn in (1).
Because the binomial distribution is fairly symmetric, the most probable number of blacks (an integer) is very close to the average
number of blacks (a non-integer). The average number of blacks is pB N. For the cases we consider, we can without error take the
most probable number of blacks to be pB N rounded to the nearest integer.

We cannot proceed much further without a value for pB , the probability that a randomly selected inmate is black. This probability
varies from state to state depending on the population mix. States with few blacks will have fewer blacks on death row. Rev.
Jackson would argue that pB is the black population fraction of the state, but of course that is not so. The probability, pB , is the
black fraction of capital murderers, a vastly different number.

For convenience, assume that the black fraction of capital murderers
is equal to that of other murderers.Let NBM be the number of black murderers and NWM the number of white murderers in
a given state. Then for that state,

We define the per capita black to white murder-rate ratio, R ,

where NB and NW are the
black and white populations, respectively, in the state. Evidence suggests that criminal
behavior and consequently R , is more characteristic of race than of geography. In fact, data show R to be essentially invariant
to crossing state boundaries, its value falling between 7 and 8. That is, a black is between 7 and 8 times more likely than a white to be a
murderer. The quantity, R, may be evaluated from population and crime databases.

Because the per capita black to white murder-rate ratio, R , is nearly constant,
we find it convenient to express pB in terms of it. From (3)
and (4) we write

Though R remains constant, the population ratio, NW / NB , varies by state. In Figure 1, using a value of 7.5 for R, we see how the
probability of a random death-row inmate being black varies with a state's population mix.

Is Death Row Too Black?We illustrate how to test for bias on death-row using data from Alabama. We consider only non-Hispanic whites and non-Hispanic blacks.
Accordingly, the terms white and black, as we use them below, do not include Hispanics of any race.

As of April 1, 2000, Alabama held under sentence of death 97 whites and 86 blacks. Following Rev. Jackson, we observe that African
Americans are 26 percent of Alabama's population, but 47 percent of death row.
(Our numbers are more recent and thus differ a bit
from Jackson's. The newer data are even more objectionable from his vantage.) But is Alabama's
death row really too black as Jackson alleges?

Using in (5) a value of 7.5 for the black to white per capita homicide ratio, R, we find the probability, pB ,
of a random death-row
inmate in Alabama being black to be 0.729. That is, "on average" we should find 72.9 percent
of Alabama's death row to be black. If the
Alabama justice system were bias free, the most probable number of blacks in its 183 prisoner death-row would be (0.729)(183) or
133. With only 86 blacks under sentence of death, Alabama's death row is too white -- much too white!

How unlikely is Alabama's death row? Statistical fluctuations normally produce clustering about most probable values. In statistical
terms, the best question to ask is how many standard deviations (SD) from the most probable number of blacks (133) is the actual
number (86)? The standard deviation, σ, of a binomial distribution is given by

For Alabama, N = 183 and pB = 0.729, yielding σ = 6.01. Thus the number of blacks on death row
is (133-86)/6.01 or
7.8 SD away from the most probable number (133). The likelihood of finding this number of blacks (or fewer) on death row
by chance is 1 in ~1014. Not only do we find the sentence of death in Alabama to be biased against white suspects, it is
extraordinarily so.

We subjected each state, with a death penalty, to similar analysis.
In some states a small black population precluded a meaningful statistical analysis. (For example,
only 1 in ~1700 Idahoans is black.) Still other states have death rows too
small or with too few blacks to obtain useful results. For those states meeting the statistical requirements, we summarize
our findings in Tables 2, 3 and 4.

Table 2
States Biased Against White Suspects

State

white
non-Hispanic
population

black
non-Hispanic
population

No. of
white
inmates

No. of
black
inmates

No. of
std dev
from most
probable
death-row
composition

Probability
of this
number or
fewer
blacks

Florida

10,275,486

2,159,631

213

139

8.3

5 x 10-17

Alabama

3,149,149

1,132,330

97

86

7.8

3 x 10-15

Georgia

5,162,469

2,206,922

70

64

7.7

7 x 10-15

Mississippi

1,708,949

1,005,812

29

34

5.5

2 x 10-8

South Carolina

2,637,674

1,148,558

35

35

5.4

3 x 10-8

Tennessee

4,446,526

903,647

60

34

4.9

5 x 10-7

North Carolina

5,607,335

1,662,781

87

127

3.1

0.001

Virginia

4,977,060

1,351,857

16

11

2.9

0.002

Texas

11,088,296

2,235,697

166

188

2.7

0.003

Kentucky

3,608,321

283,584

33

8

2.3

0.01

Louisiana

2,780,165

1,398,315

26

61

2.1

0.02

Table 3
States Biased Against Black Suspects

State

white
non-Hispanic
population

black
non-Hispanic
population

No. of
white
inmates

No. of
black
inmates

No. of
std dev
from most
probable
death-row
composition

Probability
of this
number or
fewer
whites

Pennsylvania

10,327,614

1,119,161

70

146

6.7

1 x 10-11

Table 4
Unbiased States

State

white
non-Hispanic
population

black
non-Hispanic
population

No. of
white
inmates

No. of
black
inmates

No. of
std dev
from most
probable
death-row
composition

Illinois

8,637,209

1,770,975

53

106

1.6

California

16,526,103

1,807,451

229

207

1.1

Arizona

3,229,355

101,020

82

14

1.0

Delaware

561,967

145,359

8

10

1.0

Indiana

5,230,975

484,226

28

14

1.0

New Jersey

5,568,157

1,055,918

9

7

1.0

Missouri

4,688,237

606,441

45

37

0.7

Nevada

1,271,473

112,337

45

35

0.7

Maryland

3,324,098

1,423,189

5

13

0.6

Oklahoma

2,672,765

240,763

79

49

0.5

Arkansas

2,060,075

404,814

16

24

0.0

Ohio

9,632,946

1,282,831

98

98

0.0

Bias and GeographyAn unexpected geographic pattern of bias emerged from the calculations. States biased against white suspects cluster in the South,
and stretch west into Texas. Moving north, a band of race-neutral states materializes. Only one state, Pennsylvania, is biased against
black suspects. The pattern of bias is mapped in Figure 2.

Death-Row DetailsOur "integral" approach to death-row bias revealed it and also located it geographically. To learn more, we
must turn to "differential" studies, which operate conventionally by throwing hundreds of variables into a regression engine. Of this
genre, the most cited study (and perhaps the best) is by University of Iowa law professor, David Baldus. Baldus with his colleagues
conducted a massive statistical investigation of capital cases in Georgia in the seventies. By controlling an extensive list of variables
including aggravating factors, race of the murderer and victim, number of victims, jury composition and more, they demonstrated (at
least in Georgia) that the race of the victim, much more than that of the accused, influences the outcome of capital cases. Specifically, they
found that a murder suspect is most likely to be charged with capital murder if his victim is white. He is also more
likely to receive a death sentence for killing a white. The suspect's race is minimally important. Simply put, white victims are "valued"
more than black victims in Georgia. Evidence suggests this is true elsewhere in the South.

How then did we find a pattern of discrimination against white suspects?
Do our results conflict with those of Baldus et al? Not at all.
They are perfectly compatible. Because whites mostly kill whites and blacks mostly kill blacks, if white victims are valued more,
white perpetrators will be more likely to get a death sentence and end up on
death row. We might say that white suspects pay the price for discriminating against black victims. The eminent sociologist, Steven Goldberg, observes that eliminating discrimination against black victims
would have the paradoxical effect of increasing the percentage of black murderers sentenced to death.

Lawyers and Mathematicians: Two PerspectivesThe Legal Defense Fund of the NAACP says of the Baldus study,

"After reviewing over 2500 homicide cases in Georgia in the 1970's, and having controlled for 230 non-racial factors, the study
concluded that a person accused of killing a white was 4.3 times more likely to be sentenced to death than a person accused of killing
a black."

And from the ACLU:

"Professor David Baldus examined sentencing patterns in Georgia in the 1970's. After reviewing over
2500 homicide cases in that
state, controlling for 230 non-racial factors, he concluded that a person accused of killing a white was 4.3 times more likely to be
sentenced to death than a person accused of killing a black."

The NAACP and ACLU are working from the same
script. It is a script used by many death-penalty opponents, because they all take their
cues from the same source: the Supreme Court ruling in McCleskey v. Kemp (1987). Justice Powell wrote for the majority:

"One of [Baldus'] models concludes that, even after taking account of 39 nonracial variables, defendants charged with killing white
victims were 4.3 times as likely to receive a death sentence as defendants charged with killing blacks."

But the Court made a boo boo. After so many years, death-penalty opponents should know that the Supreme Court confused odds
with probability. (For more about this, see Arnold Barnett's delightful article, How Numbers Deceive.) Baldus
found that the odds
(not the probability) of receiving a death sentence were 4.3 times greater for a defendant charged with killing a white than for killing a black.

Odds are defined as probability divided by (1 minus probability). If you do the arithmetic, you will find that the probability of a death
sentence for killing a white victim, PWV , is not 4.3 times the probability, PBV
, for killing a black.
The two probabilities are related as
follows:

Figure 3 graphically illustrates 1)
what Baldus meant, 2) what the Court said he meant, and 3) how
each relates to bias-free justice.

From Figure 3 we see that the probability of receiving a death sentence for killing a white victim was greatly exaggerated by the
Court. Only when the chance of a death sentence is very small (i.e., not many aggravating circumstances) is the factor of 4.3
approached. But since the death penalty is not likely to be imposed under these circumstances,
the victim's race becomes moot. None of this is to say that the victim's race is unimportant. In the gray area where the death penalty is neither very likely nor very
unlikely, it is a factor, not as big as the Court supposed,
but enough to account for the bias observed in the
South. There is no need for the NAACP, ACLU and others to build on the Court's
error.

More than a decade has elapsed since McCleskey v. Kemp,
yet the NAACP and ACLU continue to trumpet the Court's false conclusion. They
entertain not only false, but dishonest
uses of the sources from which they draw support. We harbor no such
inclinations, seeking only to clarify, and to communicate the results of our
inquiries to a world thirsty for
Griffian knowledge. Being thus limited, questions remain unanswered -- two in particular: Why is the South unique among regions for death-row discrimination? And, what
is it about Pennsylvania, that it stands alone among
states by discriminating against black homicide suspects? We invite the reader
to contribute
$0.02.